Search results
Results from the WOW.Com Content Network
Fuzzy clustering (also referred to as soft clustering or soft k-means) is a form of clustering in which each data point can belong to more than one cluster.. Clustering or cluster analysis involves assigning data points to clusters such that items in the same cluster are as similar as possible, while items belonging to different clusters are as dissimilar as possible.
Variations of k-means often include such optimizations as choosing the best of multiple runs, but also restricting the centroids to members of the data set (k-medoids), choosing medians (k-medians clustering), choosing the initial centers less randomly (k-means++) or allowing a fuzzy cluster assignment (fuzzy c-means). Most k-means-type ...
In statistics, k-medians clustering [1] [2] is a cluster analysis algorithm. It is a generalization of the geometric median or 1-median algorithm, defined for a single cluster. k-medians is a variation of k-means clustering where instead of calculating the mean for each cluster to determine its centroid, one instead calculates the median.
Fuzzy C-Means Clustering is a soft version of k-means, where each data point has a fuzzy degree of belonging to each cluster. Gaussian mixture models trained with expectation–maximization algorithm (EM algorithm) maintains probabilistic assignments to clusters, instead of deterministic assignments, and multivariate Gaussian distributions ...
The starting point for this new version of the validation index is the result of a given soft clustering algorithm (e.g. fuzzy c-means), shaped with the computed clustering partitions and membership values associating the elements with the clusters. In the soft domain, each element of the system belongs to every classes, given the membership ...
In mathematics, fuzzy measure theory considers generalized measures in which the additive property is replaced by the weaker property of monotonicity. The central concept of fuzzy measure theory is the fuzzy measure (also capacity, see [1]), which was introduced by Choquet in 1953 and independently defined by Sugeno in 1974 in the context of fuzzy integrals.
Type-2 fuzzy sets and systems generalize standard Type-1 fuzzy sets and systems so that more uncertainty can be handled. From the beginning of fuzzy sets, criticism was made about the fact that the membership function of a type-1 fuzzy set has no uncertainty associated with it, something that seems to contradict the word fuzzy, since that word has the connotation of much uncertainty.
The k-medoids problem is a clustering problem similar to k-means. The name was coined by Leonard Kaufman and Peter J. Rousseeuw with their PAM (Partitioning Around Medoids) algorithm. [ 1 ] Both the k -means and k -medoids algorithms are partitional (breaking the dataset up into groups) and attempt to minimize the distance between points ...